- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 3
- A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spa...
A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces
Authors : Ömer Faruk Doğan
Pages : 811-820
Doi:10.15672/hujms.768123
View : 10 | Download : 3
Publication Date : 2021-06-07
Article Type : Research
Abstract :We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into harmonic Bergman-Besov spaces $b^{q}_{\beta}$, weighted Bloch spaces $b^{\infty}_{\beta} $ or the space of bounded harmonic functions $h^{\infty}$, allowing the exponents to be different. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.Keywords : integral operator, harmonic Bergman-Besov kernel, harmonic Bergman-Besov space, weighted harmonic Bloch space, harmonic Bergman-Besov projection